Apparatus for obtaining a conoscopic holograph using incoherent light is described in patent document U.S. Pat. No. 4,602,844. The apparatus described in that document includes, as illustrated diagrammatically in accompanying FIG. 1, a birefrigent crystal inserted between two circular polarizers, and a photosensitive element constituting a recording medium.
In document U.S. Pat. No. 4,602,844, the axis of the crystal is parallel to the geometrical axis of the system, i.e. perpendicular to the recording medium.
This crystal decomposes an incident ray firstly into an ordinary ray subjected to a refractive index n.sub.o, and secondly into an extraordinary ray subjected to a refractive index which varies as a function of the angle of incidence .theta., with this variable refractive index being written n.sub.e (.theta.).
These two rays propagate at different speeds within the crystal. As a result they are at different phases on leaving the crystal. Conoscopic holography is based on the fact that this phase difference is a function of the angle of incidence .theta.. The two rays interfere on the recording medium (photographic film, CCD, . . . ) after passing through the outlet polarizer such that the intensity of the resulting ray is also a function of the angle .theta.. In other words, unlike conventional holography, each incident ray produces its own reference ray. The set of rays situated on a cone whose axis is parallel to the optical axis of the crystal and having an aperture angle .theta. will give the same intensity on the observation plane.
As shown in accompanying FIG. 2, the conoscopic hologram of a point obtained by means of the above-mentioned apparatus corresponds to a zoned grating, i.e. to a series of concentric angular interference fringes.
The conoscopic hologram of an object is the superposition of the holograms of each of the points constituting the object. FIGS. 3b and 3c of the above-mentioned patent Document U.S. Pat. No. 4,602,844 respectively show holograms for two points and for three points of a plane object.
The resulting hologram contains all of the useful information, such that it is possible to reconstruct the initial object in three dimensions.
The conoscopic system performs a linear transformation between the object and its hologram.
The impulse response of the system which characterizes the linear transformation is written: EQU T(x',y')=1+cos (.alpha.r.sup.2) (1)
where r.sup.2 =x'.sup.2 +y'.sup.2, and: EQU .alpha.=2.pi.L.multidot..delta.n/.lambda.n.sub.o.sup.2 Z.sub.c.sup.2,(2)
with
.lambda.=source wavelength PA1 L=crystal length PA1 n.sub.o =the ordinary index of the crystal PA1 .delta.n=the absolute value of the difference between the ordinary index and the extraordinary index PA1 x,y,z=coordinates in the object volume PA1 x',y'=coordinates in the hologram plane EQU Z.sub.c .apprxeq.Z(x,y)-L+L/n.sub.o ( 3)
where Z(x,y) is the distance between the holographic plane and the object under consideration, situated at the lateral position (x,y). The Fresnel parameter .alpha. can also be written: EQU .alpha.=.pi./.lambda..sub.eq (Z.sub.c)Z.sub.c ( 4)
thus defining an equivalent wavelength .lambda..sub.eq : EQU .lambda..sub.eq =.lambda.n.sub.o.sup.2 .multidot.Z.sub.c /.delta.n2L or:(5) EQU .alpha.=.pi./.lambda.f.sub.c ( 6)
thus defining the focal length f.sub.c of the Fresnel lens: EQU f.sub.c =n.sub.o.sup.2 .multidot.Z.sub.c.sup.2 /.delta.n2L (7)
When the object under consideration is plane (.alpha.=constant) the equivalent wavelength and the focal length f.sub.c are constants of the system.
Equation (4) then shows that the conoscopic hologram of a point recorded at a wavelength .lambda. is similar to the hologram of the same point recorded using coherent light (Gabor holography) at the equivalent wavelength .lambda..sub.eq. It should be observed that the conoscopic hologram measures intensities and not amplitudes.
Since the distances Z.sub.c and L are of the same order of magnitude and since .delta.n is about 0.1, the wavelength .lambda..sub.eq is greater than the real wavelength .lambda. at which recording takes place: typically .lambda..sub.eq =3 .mu.m to 100 .mu.m.
As a result, the lateral resolution of the hologram (proportional to the wavelength .lambda.) is less in conoscopic holography than in conventional holography. Its value lies around a few tens of micrometers.
As mentioned above, a hologram recorded using a conoscopic device contains all of the useful information.
For example, for a hologram of a point corresponding to a zoned grating:
the center of the zone and the object point lie on the same straight line parallel to the optical axis, and if the object point is translated transversely or laterally, then the hologram is translated identically in the holographic plane. The coordinates of the center C(x.sub.o,y.sub.o) of the Fresnel zone are thus equal to the first two coordinates of the holographed point P(x.sub.o,y.sub.o,z.sub.o);
the intensity of the hologram gives the light energy in the light aperture cone; and
the spacing of the fringes gives the distance between the object and the observation plane, independently of the position of the conoscopic apparatus.
The following may be written: EQU Z.sub.c =R.sup.2 /F.lambda..sub.eq ( 8)
and EQU Z(x,y)=Z.sub.c +L-L/n.sub.o =R.sup.2 /F.lambda..sub.eq +L-L/n.sub.o( 9)
where R is the radius of the Fresnel zone and F is the number of light and dark fringes on the radius.
In spite of the great hopes based on conoscopic holography as described above, it has not yet led to industrial developments.
This appears to be due to the fact that it is relatively difficult to make use of a hologram made in this way.
The object of the present invention is to propose means enabling such a hologram to be made use of more simply.